Problem: Divide the following complex numbers: $\dfrac{12(\cos(\frac{3}{4}\pi) + i \sin(\frac{3}{4}\pi))}{6(\cos(\frac{2}{3}\pi) + i \sin(\frac{2}{3}\pi))}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $12(\cos(\frac{3}{4}\pi) + i \sin(\frac{3}{4}\pi))$ ) has angle $\frac{3}{4}\pi$ and radius 12. The second number ( $6(\cos(\frac{2}{3}\pi) + i \sin(\frac{2}{3}\pi))$ ) has angle $\frac{2}{3}\pi$ and radius 6. The radius of the result will be $\frac{12}{6}$ , which is 2. The angle of the result is $\frac{3}{4}\pi - \frac{2}{3}\pi = \frac{1}{12}\pi$ The radius of the result is $2$ and the angle of the result is $\frac{1}{12}\pi$.